Aggregate Fineness Modulus

The sieve stack is done, the balance has given the mass retained on each screen, and what is missing is the figure that goes on the report. Fineness modulus is that figure: a whole grading curve compressed into two decimals, used to judge whether a sand suits the mix and to compare one truckload against the next from the same pit. Getting it wrong shows up fast — sand that runs too fine pulls extra water and cement for the same workability, sand that runs too coarse leaves a harsh mix prone to segregation and bleeding. The arithmetic trips people up, since it wants cumulative retained values, and only from the standard sieve series.

FM = sum of cumulative percentages retained ÷ 100, over the standard series: 19, 9.5, 4.75, 2.36, 1.18, 0.6, 0.3 and 0.15 mm. Cumulative means the amount held on that sieve plus everything held on every coarser sieve, so the sequence always rises as the openings shrink. The values on screen — 0, 0, 2, 12, 30, 55, 80 and 94 — add up to 273 and yield FM 2.73, inside the 2.20 to 2.90 optimum band of Brazilian standard NBR 7211; the usable band stretches from 1.55 to 3.50. Since each sieve doubles the opening of the next, one whole point of modulus corresponds to doubling the average grain size. Coarse aggregate in the 9.5 to 25 mm range typically lands between 6.8 and 7.0.

A summary throws information away: two sands with very different curves can both land on 2.73, one well graded, one gap graded. That is why the standard asks for the curve and the zone limits, not the figure alone. This page covers 19 mm down to 0.15 mm, enough for sand and for small coarse aggregate; grains above 19 mm also need the 37.5 and 75 mm sieves, and leaving those out understates the answer. Intermediate series sieves such as 25, 12.5 and 6.3 mm play no part in the modulus and inflate it if added. Percentages outside 0 to 100 trigger the warning, and a sequence that stops rising usually means individual retained values went in where cumulative ones belong.